Aircraft Weight and Balance Calculations: Mass, CG and Load Problems

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Aircraft Weight and Balance Calculations

The following problems cover maximum structural mass, centre of gravity (CG), fuel and payload calculations, floor load limits and helicopter mass problems.

Maximum Load and Structural Limits

  • The maximum load is 350 kg/m; 400 kg dimension 1.2 m.
  • Given maximum structural take-off mass 48000 kg: 47800 kg.
  • The maximum zero fuel mass: 1, 3, 5.
  • Given maximum structural take-off mass 146000 kg: 120300 kg.
  • Given maximum structural take-off mass 72000 kg: 69600 kg.
  • Given maximum structural take-off mass 146900 kg: 120900 kg.
  • Given maximum structural take-off mass 8600 kg: 7340 kg.
  • " " 8350 kg: 7000 kg.
  • " " 7400 kg: 6625 kg.

Centre of Gravity Problems

  • An aircraft has its centre of gravity at 7 m with a weight of 49000: 343000 Nm.
  • The loaded centre of gravity 713 mm: 16%.
  • Given aeroplane mass 36000 kg: 0.31 m.
  • Given information: Basic empty 12045 + 30 + 361350: 56.53 cm aft of datum.
  • " " : 24 cm aft of datum.
  • Calculate centre of gravity, datum centre of gravity 12.53 m: 36.3%.
  • At given CG 15% MAC 134.5 inch: 645.78 inch aft of datum.
  • A mass of 500 kg located 10 m: 80000 Nm.
  • The mass of an aircraft is 1950 kg: 33 cm.
  • Basic mass 1200 kg; basic balance 3.00 m: 22%.

Dry Operating and Zero Fuel Mass

  • Given total mass 2900 kg: 207 kg.
  • Given total mass 7500 kg: 62.5 kg.
  • Given dry operating mass 29800 kg: 12900 kg.
  • The total mass of an aircraft is 9000 kg, position 2.0 m: 300 kg.
  • Given total mass 112000: 29344 kg.
  • Given dry operating mass 38000 kg: 71300 kg and 23000 kg.
  • Zero fuel mass 4920 kg: 6225 kg.
  • Zero fuel mass 4770 kg: 6710 kg.
  • Zero fuel mass 6660 kg: 8175 kg.
  • Dry operating mass 5210 kg: 1020 kg.
  • " " 4920 kg: 820 kg.
  • " " 5320 kg: 1470 kg.
  • Dry operating mass 34900 kg; take-off mass 66300 kg: 12700 kg.
  • The dry operating mass 2000 kg: 1000 kg.

Take-Off and Landing Mass

  • The take-off mass 117000 kg: 53000 kg.
  • The take-off mass 141000 kg, fuel 63000: 79000 kg.
  • Take-off mass 67200 kg; limited landing mass 54200 kg: 13090 kg.
  • Take-off mass 302550 kg, fuel 121450 kg: 141100 kg.
  • Landing mass 54230 kg: 29280 kg.
  • Limited take-off mass 89200 kg: 21080 kg.
  • Certified maximum take-off 141500 kg; limited take-off 137300 kg: 78900 kg.
  • Maximum ramp mass 69900 kg; maximum take-off mass 69300 kg: 17840 kg.
  • Limited take-off mass 93500 kg, landing mass 81700 kg: 87300 kg and excess.
  • Take-off runway limit 185000 kg; landing runway 180000 kg: 54000 kg.
  • Block fuel 40000 kg; trip fuel 29000 kg: 32100 kg.
  • Dry operating mass 90000 kg; block fuel 30000 kg: 25800 kg.

Fuel Calculations

  • The maximum fuel is 3800 US gallons: 11364 kg.
  • Flight London to Valencia 20100 l: 14331 kg.
  • What is the mass of aviation fuel F34 if 170 l is refuelled? 133 kg.

Floor Load and Package Limits

  • The maximum floor loading 750 kg; a package 600 kg: 40 cm by 200 cm.
  • The maximum intensity 650 kg, dimension 80 cm by 80 cm: 416.0 kg.
  • The floor limit hold 5000 N/m2: 80 kg.
  • The floor of the main deck 4000 N/m2: 100 kg.
  • A pallet having 100 cm x 150 cm: 20 kg may be added.

Helicopter Mass and Balance

  • At a mass of 1800 kg, a helicopter: 1.5 cm right.
  • The following weighing helicopter front point 220 kg: 3.44 m.
  • " " 300 kg: 4 cm right.
  • After weighing helicopter forward point: 350 kg, 4.52 m.
  • Length of the mean aerodynamic chord 1 m: 110 kg.
  • The baggage compartment helicopter 1.2 wide, 1.4 m: 840 kg.
  • " " 2.2 " : 1478 kg.
  • " " 1.2 " 2.4 m: 1497 kg.
  • " " 1.1 " 1.4 m: 462 kg.
  • The take-off mass helicopter 8420 kg: 5630 kg.
  • " " 8600 kg: 5480 kg.
  • " " 8210 kg: 4880 kg.
  • " " 7840 kg: 6010 kg.
  • " " 8470 kg: 6899 kg.
  • " " 9000 kg: 7120 kg.
  • " " 6700 kg: 5919 kg.
  • The basic empty mass helicopter 4615 kg: 5064 kg.
  • " " 5322 kg: 5773 kg.
  • " " 5480 kg: 5781 kg.
  • " " 4910 kg: 3070 kg.
  • " " 4610 kg: 2350 kg.
  • " " 5200 kg: 2640 kg.
  • The maximum fuel loaded helicopter given 2200 l: 1738 kg.
  • " " given 1120 l: 885 kg.
  • " " given 565 l: 446 kg.
  • " " given 800 US gallons: 2392 kg.
  • " " given 600 US gallons: 1794 kg.
  • " " given 400 US gallons: 1196 kg.
  • A helicopter to a landing mass of 7550 kg: 2780 kg.
  • " " : 2680 kg.
  • " " 7350 kg: 3210 kg.
  • " " 6930 kg: 2670 kg.
  • The following data helicopter which maximum structural take-off 86400 kg: 3650 kg.
  • " " 7400 kg: 2670 kg.
  • " " 8400 kg: 3150 kg.
  • The crew transport helicopter, data block fuel 1650 kg: 1675 kg.
  • " " 1270 kg: 2155 kg.
  • " " 1490 kg: 1640 kg.
  • " " 5040 kg: 905 kg.
  • " " 4920 kg: 1620 kg.
  • " " 5210 kg: 2275 kg.
  • Take-off mass helicopter 8400 kg, traffic load 1590 kg: 4970 kg.
  • " " 8150 kg, 990 kg: 4760 kg.
  • " " 8340 kg, 1870 kg: 4780 kg.
  • Prior transport helicopter maximum fuel 2367 l, density 0.79: 1665 kg.
  • " " : 1620 kg.
  • " " 2244 l: 712 kg.
  • A transport helicopter tank capacity 2532 l, take-off 8240 kg: 2000 kg.
  • " " 7480 kg: 1660 kg.
  • " " 8300 kg: 1400 kg.
  • A helicopter departs, take-off mass 8220 kg, fuel 1750 kg: 1130 kg.
  • " " 8600 kg, fuel 1840 kg: 1380 kg.
  • " " 8040 kg, fuel 1750 kg: 730 kg.
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